Adding tracks/markers with a custom name?
add_marker_at_click() is modal operator so it seems that it returns 'RUNNING_MODAL' and keeps running (waiting for user interactions) while your operator will finish without waiting for it , so I have used add_marker() instead and changed the your operator to be a Modal operator ,also added how to pas the button name to the operator , but the problem is that i could not get the coordinates of the mouse in respect to the movie clip, so i have used the region where the movie is :

import bpy
from bpy.props import *

class AddMarker(bpy.types.Operator):
    bl_idname = "wm.addmarker"
    bl_label = "add markers with names"

    def __init__(self):
        print("Start")

    def __del__(self):
        print("End")

    x = bpy.props.IntProperty()
    y = bpy.props.IntProperty()
    name = bpy.props.StringProperty()

    def execute(self, context):
        #using 'region' in this calculation  is wrong
        self.x -=bpy.context.region.x
        self.y -=bpy.context.region.y
        x = self.x/bpy.context.region.width
        y = self.y/bpy.context.region.height
        #add marker at that position
        bpy.ops.clip.add_marker(location=(x, y))
        #rename this marker
        bpy.data.movieclips[0].tracking.tracks.active.name=self.name
        #bpy.context.scene.active_clip.tracking.tracks.active.name=self.name
        return {'FINISHED'}

    def modal(self, context, event):

        if event.type == 'LEFTMOUSE':  
            self.x = event.mouse_x
            self.y = event.mouse_y 
            self.execute(context)
            return {'FINISHED'}

        elif event.type in ('RIGHTMOUSE', 'ESC'):  
            return {'CANCELLED'}

        return {'RUNNING_MODAL'}

    def invoke(self, context, event):
        print(context.window_manager.modal_handler_add(self))
        return {'RUNNING_MODAL'}





class MARKERPANEL(bpy.types.Panel):
    bl_label = "Add markers"
    bl_space_type = "CLIP_EDITOR"
    bl_region_type = "TOOLS"
    bl_category = "MARKERPANEL"


    def draw(self, context):
        f = ['left','right','floor','corner']

        for line in f:        

            layout = self.layout
            row = layout.row()

            sc = context.space_data
            clip = context.space_data.clip
            row.operator("wm.addmarker", text=line).name = line

bpy.utils.register_class(AddMarker)
bpy.utils.unregister_class(AddMarker)       
bpy.utils.register_class(MARKERPANEL)
bpy.utils.unregister_class(MARKERPANEL)   
bpy.utils.register_module(__name__)